Certain applications for bandpass filters require variation of filter bandwidth without attendant variation in gain.
FIG. 1 shows a signal source 11 connected to a prior art bandpass filter 19. Signal source 11 generates a signal S.sub.in which has a voltage V.sub.i. Bandpass filter 19 includes a variable resistance 12 connecting signal source 11 to an output node 16 and to a resonant LC circuit 17. A signal S.sub.out having a voltage V.sub.o appears on output node 16. LC circuit 17 comprises a capacitance 13 and an inductance 14. A resistance 15 (the magnitude of resistance 15 is referred to in formulas herein as R.sub.15) represents the equivalent of the losses in LC circuit 17, and the losses in the load connected to output node 16. Signal source 11, capacitance 13, inductance 14, and resistance 15 are all connected to a reference voltage source 10.
Varying the magnitude of variable resistance 12 varies the bandwidth of bandpass filter 19 of FIG. 1. Approximately, the bandwidth of bandpass filter 19 is proportional to the multiplicative inverse of the value of variable resistance 12. However, varying resistance 12 also varies the passband gain (V.sub.o /V.sub.i) of bandpass filter 19.
FIG. 3 shows how the passband gain of bandpass filter 19 varies as a function of change in magnitude of resistance 12. An axis 82 represents the magnitude of resistance 12, an axis 81 represents the passband gain of bandpass filter 19, a line 84 is a plot of unity gain (V.sub.o =V.sub.i) and a plot 83 shows how the gain of bandpass filter 19 asymptotically approaches unity as the resistance R12 is decreased.
In order to vary bandwidth without varying passband gain, a positive feedback loop may be used.
For instance, in FIG. 2 an amplifier 27 and a resistance 28 have been added to bandpass filter 19 to form bandpass filter 29. If, for example, amplifier 27 is chosen to have a gain of 2, then resistance 28 would be chosen to have the same resistance value as resistance 15. The addition of positive feedback as in the bandpass filter 29, however, may degrade the performance of bandpass filter 19 as noise and distortion within amplifier 27 may be multiplied and appear at output node 16.